Average Error: 44.6 → 0
Time: 4.1s
Precision: 64
\[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
↓
\[-1\]
(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)
↓
-1
double f(double x, double y, double z) {
        double r17923248 = x;
        double r17923249 = y;
        double r17923250 = z;
        double r17923251 = fma(r17923248, r17923249, r17923250);
        double r17923252 = 1.0;
        double r17923253 = r17923248 * r17923249;
        double r17923254 = r17923253 + r17923250;
        double r17923255 = r17923252 + r17923254;
        double r17923256 = r17923251 - r17923255;
        return r17923256;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r17923257 = -1.0;
        return r17923257;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original44.6
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 44.6

    \[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]

  2. Simplified0

    \[\leadsto \color{blue}{-1}\]

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019112 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

  (- (fma x y z) (+ 1 (+ (* x y) z))))